Originally introduced by August Toepler in 1864 to photograph fluids of varying densities, the knife-edge technique (KET), also referred to as Schlieren photography, was adapted in the middle of the 20th century for detection and visualization of ultrasound, such as in the article “An instrument for making surface waves visible” by R. Adler et al, IEEE Trans. Son. Ultrason. SU-15 p. 157, 1968. Since then, the KET has seen a variety of applications for detection of minute perturbations, including dynamic sensors for the detection of perturbation induced by acoustic waves, as in U.S. Pat. No. 7,957,006 to the present inventor, as well as sensors for detection of perturbations of scanning devices, for example in atomic force microscopy (AFM).
Interferometry is often the intuitive selection for high resolution detection of displacement, but in different instances it can be replaced by other detection methods that are less susceptible to environmental effects. The present inventor has shown in an M.Sc. Thesis, Tel Aviv University, 1983, entitled “Optical probe for SAW velocity measurements”, that in the shot-noise limited case, the theoretical sensitivity of interferometry and the KET are identical. As such the KET, which is an incoherent detection scheme, offers many practical advantages over interferometry: it is more robust, less sensitive to environmental effects, less sensitive to the illumination source's spectral stability, insensitive to speckle which compromises the performance of coherent detection methods, and can be designed to detect perturbations in one axis. Consequently it may be a preferred method for the applications noted above as well as many others.
Reference is first made to FIGS. 1A and 1B, which illustrate schematically the use of a prior art KET system in monitoring the tilt of a surface 6. This could be the surface of an AFM cantilever, as further detailed below, or a direct surface which is perturbed, as in voice detection on the human face for example. An illuminating beam 2 is focused by means of the lens system 4 onto the surface to be monitored, and the beam reflected from the surface is directed past a knife-edge 10 to a photodetector 12. When the surface is in a first position 6, part of the reflected beam, as designated by the solid lines 16, passes the knife-edge 10 to reach the photodetector 12, and part is blocked by the knife-edge. This is shown in the end view in FIG. 1B, where the knife-edge is seen to block a certain part of the beam, shown in FIG. 1B to be approximately half of the beam. When the surface has tilted, such that it is in a second position 14, the reflected beam as designated by the dashed lines 18, has a larger part of its cross-section blocked by the knife edge, as shown in FIG. 1B, where the total power of the illumination falling on the photodetector is now reduced. The power of the illumination on the photodetector is a direct function of the tilt of the surface 6 so that monitoring the power falling on the detector corresponds to monitoring the tilt of the surface 6. If the detector power calibration as a function of surface tilt is known, then the tilt can be directly measured.
In practical systems, the measurement sensitivity can be doubled if instead of a knife-edge with a single photodetector, a split detector configuration is used. Such an arrangement is shown in the simplified schematic of FIG. 2, which, as an example, could be used for monitoring the variation in the position of the stylus tip of an atomic force microscope (AFM). In this exemplary method, light from an illumination source, such as, for example, a solid state laser or a diode laser, is reflected off the back of a cantilever and is collected by a detector having two closely spaced photosensitive areas, which will be termed separate photodiodes, even though they may be constructed on a single substrate, one designated N and the other P. The output signals from N and P are input to a differential amplifier. Angular displacement of the cantilever results in movement of the reflected laser spot over the detector surface, such that the proportions of light collected by the N and the P photodiodes changes. The output signal from the differential amplifier corresponds to the difference in power collected by each section of the photodetector, which is designated P−N. This arrangement is essentially two knife-edge detectors back-to-back, each with a signal that corresponds to the deflection of the cantilever, but opposite in sign, so that the difference of the two signals also corresponds to the cantilever movement, but with an amplitude double that that would be obtained from a single photodetector.
There are two primary modes of operation for a nanometric detection system, such as could be used as an AFM probe—the static or DC mode and the dynamic or AC mode. In the static mode, the measurement cantilever, such as that of an AFM, is “dragged” across the surface of the sample and the contours of the surface are measured directly using the deflection of the cantilever. In the dynamic mode, the cantilever is externally oscillated at or close to its fundamental resonance frequency or a harmonic. The van der Waals forces, which are strongest from 1 nm to 10 nm above the surface of the sample, or any other long range force which extends above the surface, act to decrease the oscillation amplitude and the resonance frequency of the cantilever. In an AFM, for instance, these changes in oscillation with respect to the unperturbed reference oscillation provide information about the sample's characteristics, including the sample's profile, without the need for the cantilever stylus to touch the surface. A servo mechanism can be used to maintain the resonant frequency constant by changing the distance of the cantilever from the surface, such that instead of measuring the actual distance of the stylus from the surface, the frequency feedback signal, which mirrors that change of distance can be measured.
Reference is now made to FIG. 3A, which is a graph showing the voltage output expected from the two halves of the split detector of FIG. 2, and the output from the differential amplifier which represents the difference between the two outputs, as the beam spot traverses the split detector. The output is proportional to the light power reaching the detector. For simplicity the beam is assumed to be of circular section with radius r and of uniform intensity. Under these assumptions the area of detector covered by the beam spot represents the power collected by the detector. The graph is displayed in terms of the normalized area covered by the beam spot of radius r as a function of its offset d from the center of the boundary between the two halves of the split detector, that boundary being the equivalent of the knife-edge of FIG. 1. The curve with the short dashes represents the area of the spot on the positive detector P, while the curve with the long dashes represents the area of the spot on the negative detector N. The beam spot on the split detector has a diameter 2r, and the split sections of the detector are each 2r high as seen in FIG. 3B. The width of the detector in the dimension parallel to the boundary of the split detectors may be larger than 2r so the beam on each detector section is maintained at a relatively large distance from the detector's edge in the lateral dimension, ensuring that any lateral misalignment does not compromise the integrity of the signal. In other words, the fractional area of the beam on each detector section is directly related to the displacement d of the center of the beam from the boundary of the split detectors. When the beam spot is centered on the pair of photodetectors, i.e. for d=0, the beam is split equally between the P and N parts of the photodetector (left-most image of FIG. 3B), corresponding to the point of the graph of d/r=0, where it is seen that each section shows half the power of the beam (expressed in values of half the area of the beam spot, πr2/2=1.57 r2, which is normalized to 1.57 on the graph). The axes of the graph of FIG. 3A are normalized to multiples of r (offset axis) and multiples of r2 (illuminating power or corresponding output voltage axis).
Typically, the KET is used to detect small signals. Ideally the setup is arranged so that the illumination spot is centered on the split detector. At this location of the beam, as further explained below, the sensitivity is maximal. FIG. 3C shows schematically that a small perturbation, θ0 cos ωt, about an operating point close to d=0, introduces a corresponding signal θ0α cos ωt, at the output, where α represents the slope of the graph at the operating point. The output signal is proportional to the slope of the curve, and the maximal sensitivity occurs where the slope is maximal. It is also apparent from the graph that the sensitivity gradually reduces as the illumination spot is allowed to move away from the center, d=0: the slope of the curve in FIG. 3C is reduced with increasing distance from d=0, reaching zero sensitivity where the slope becomes zero at the positive and negative peaks of the graph. In other words the sensitivity of the KET detection drops off at an increasing rate as the setup departs from the optimal operation position at d=0 and the beam spot is allowed to shift away from the center of the detector. Consequently, to ensure a minimal working sensitivity the shift of the spot from the center of the detector should be limited. This permitted shift from the center of the detector is regarded as the dynamic range for alignment of the KET sensor. As is shown hereinbelow, this dynamic setup range is proportional to the sensitivity of the KET: the more sensitive the KET detection, the tighter the tolerance for the KET standoff from the center. It is the purpose of this invention to alleviate this limitation of tight setup tolerance while maintaining the higher detection sensitivity.
Referring back again to FIG. 3B, and looking first at the output from the positive element, P, as the spot moves away from d=0 to cover a larger portion of P, the area of the spot on P increases, indicating that power on P increases and hence the voltage generated by P increases, until all of the spot is located squarely on the P side of the detector. At this point, d=r, the area illuminating P is πr2=3.14 r2 which is normalized to 3.14 on the graph (see second image from left of FIG. 3B). As the spot continues to move away from the center of the split detector, the area of the spot covering the P section now decreases through the point where it is half on the P detector section (at d=2r, third image from the left of FIG. 3B) until it is completely off the detector at d=3r where the area of P that is illuminated reaches 0 (right image of FIG. 3B). Similarly, when the detector spot moves in the opposite direction from d=0, the signal decreases until the beam is completely off the P section of the detector at d=−r, where the P signal becomes zero. At this same point the beam is completely located over the N section of the detector so that here the N section output is maximum, with a signal proportional to 3.14r2. The signal from the N section varies with the location of the illumination spot on the detector, d, in the same form as the P section signal, but it is inversed in sign and shifted, as is shown in the graph of FIG. 3A.
The output from the difference amplifier, representing the voltage P−N, is shown by the solid line in FIG. 3A, and as is observed in the graph, at the most sensitive location d=0, this P−N output has twice the slope of either the P output or the N output alone. The split detector configuration thus doubles the detection sensitivity of this virtual knife-edge configuration. The small signal sensitivity is proportional to the slope of the graph, and is maximum at d=0. The slope of the graph, and the small signal sensitivity, reach 0 at d=±r. Here two setup ranges are defined: the setup sensitivity range (SSR), spanning the entire range where any signal is obtained, and the setup dynamic range (SDR), confined to the setup range where a workable signal with good sensitivity is obtained. The SSR of the graph of FIG. 3A, is 6r, but it includes regions where there is very low sensitivity (around d=±r and d=±3r), and regions where the sign of the signal is inverted (where the slope is negative) in the regions −3r<d<−r and r<d<3r. The workable SDR may be defined as the region where the signal remains of the same sign and sensitivity drops monotonically to 50%. In the case of the graph of FIG. 3A the SDR is limited to approximately d=±0.9r. In other words the SDR for the split detector KET is 1.8r, or 90% of the diameter of a uniform beam spot. Note that, outside the SDR defined above, the output signal is both opposite in sign to that within the SDR and smaller than the signal within the SDR: is can be seen that the slopes of the response curves outside the SDR are necessarily less than 50% of the slope at the center of the detector at d=0. The above discussion is simplified under the assumption of a uniform, circular illumination spot with a sharp boundary. It is noted that using a more realistic beam illumination spot distribution, such as, for example, a Gaussian intensity distribution, similar characteristics to those of the simplified model above are obtained, but the graphs of FIG. 3A would have a “longer tail” extending beyond d=±3r. Therefore, it would be more accurate to use a detector having split sections of height somewhat more than 2r, where 2r would be the diameter of a spot having an equivalent top-hat profile. Nevertheless, the behavior and values of the graphs in the central portion for −r≤d≤r would be very similar and therefore the simplified analysis with a uniform beam spot is a good predictor of the practical performance of the performance of the split detector KET.
The discussion above relates to a KET detection system that is sensitive to angular perturbations of the detection surface 6 in FIG. 1. Slightly modified arrangements offer detection of perturbation normal to the surface, as described, for example in the above mentioned U.S. Pat. No. 7,957,006. Irrespective of such modifications to the KET arrangement, the nature of the detected signals is identical to those considered above, so that the discussion above and the present disclosure apply equally well to KET arrangements for detection of normal surface perturbations.
As described above, the SDR of a split detector KET is related to its sensitivity. In practice sensitivities as high as possible are sought. To increase the sensitivity, the spot size may be reduced and the length of the detection path, shown in the example of FIG. 1 as the distance between the tilting surface 6 and the plane of the knife-edge 10, increased. The spot size defines the dynamic range at approximately 0.9 of its diameter, and the length of the detection path increases the shift, d, for a given displacement of the surface 6. For very high sensitivities the alignment tolerance, or SDR, of the KET becomes impractical. This limitation severely curtails the usefulness of the knife edge technique, despite its simplicity and high sensitivity.
There therefore exists a need for a knife-edge configuration which overcomes at least some of the disadvantages of prior art systems and methods, in particular in providing a larger dynamic range to the detection arrangement.
The disclosures of each of the publications mentioned in this section and in other sections of the specification, are hereby incorporated by reference, each in its entirety.